标题： 关于类型A中的自正规化Sylow$2$-子群 显示英文标题

标题： On Self-Normalising Sylow $2$-Subgroups in Type A

摘要： Navarro 提出了一个有限群$G$拥有自正规化西洛$2$-子群的必要且充分条件，该条件是通过$G$的普通不可约特征标给出的。 第一位作者将该猜想的证明简化为当$G$是拟单时，证明某些相关陈述成立。 在本文中我们证明，当$G/Z(G)$是$\mathrm{PSL}_n(q)$、$\mathrm{PSU}_n(q)$或者在特征为$2$的有限域上定义的单李型群时，这些条件都满足。 显示英文摘要

摘要： Navarro has conjectured a necessary and sufficient condition for a finite group $G$ to have a self-normalising Sylow $2$-subgroup, which is given in terms of the ordinary irreducible characters of $G$. The first-named author has reduced the proof of this conjecture to showing that certain related statements hold when $G$ is quasisimple. In this article we show that these conditions are satisfied when $G/Z(G)$ is $\mathrm{PSL}_n(q)$, $\mathrm{PSU}_n(q)$, or a simple group of Lie type defined over a finite field of characteristic $2$.